The Mirrors Model : Macroscopic Diffusion Without Noise or Chaos

We first clarify through classical examples the status of the laws of macroscopic physics as laws of large numbers. We next consider the mirrors model in a finite $d$-dimensional domain and connected to particles reservoirs at fixed chemical potentials. The dynamics is purely deterministic and non-ergodic. We study the macroscopic current of particles in the stationary regime. We show first that when the size of the system goes to infinity, the behaviour of the stationary current of particles is governed by the proportion of orbits crossing the system. This allows to formulate a necessary and sufficient condition on the distribution of the set of orbits that ensures the validity of Fick's law. Using this approach, we show that Fick's law relating the stationary macroscopic current of particles to the concentration difference holds in three dimensions and above. The negative correlations between crossing orbits play a key role in the argument

Multistability and memory effect in a highly turbulent flow: experimental evidence for a global bifurcation

We report an experimental evidence of a global bifurcation on a highly turbulent von Karman flow. The mean flow presents multiple solutions: the canonical symmetric solution becomes marginally unstable towards a flow which breaks the basic symmetry of the driving apparatus even at very large Reynolds number. The global bifurcation between these states is highly subcritical and the system thus keeps a memory of its history. The transition recalls low-dimension dynamical systems transitions and exhibits a very peculiar statistics. We discuss the role of turbulence in two ways: the multiplicity of hydrodynamical solutions and the effect of fluctuations on the nature of transitions.Comment: submitted to Physical Review Letters 19 May 2004, accepted 10 September 200

Ambivalent effects of added layers on steady kinematic dynamos in cylindrical geometry: application to the VKS experiment

The intention of the ''von Karman sodium'' (VKS) experiment is to study the hydromagnetic dynamo effect in a highly turbulent and unconstrained flow. Much effort has been devoted to the optimization of the mean flow and the lateral boundary conditions in order to minimize the critical magnetic Reynolds number and hence the necessary motor power. The main focus of this paper lies on the role of ''lid layers'', i.e. layers of liquid sodium between the impellers and the end walls of the cylinder. First, we study an analytical test flow to show that lid layers can have an ambivalent effect on the efficiency of the dynamo. The critical magnetic Reynolds number shows a flat minimum for a small lid layer thickness, but increases for thicker layers. For the actual VKS geometry it is shown that static lid layers yield a moderate increase of the critical magnetic Reynolds number by approximately 12 per cent. A more dramatic increase by 100 until 150 per cent can occur when some rotational flow is taken into account in those layers. Possible solutions of this problem are discussed for the real dynamo facility.Comment: 24 pages, 11 figures, minor changes, to appear in European Journal of Mechanics B/Fluid

Supercritical Eckhaus Instability for Surface-Tension-Driven Hydrothermal Waves

International audienceWe study the nonlinear dynamics of hydrothermal waves produced by a surface-tension-driven convective flow in a long and thin annular channel heated from the side. Above onset, the supercritical traveling wave pattern undergoes a secondary instability: a supercritical Eckhaus instability. This leads to a small-wave-number phase-modulated nonlinear mode, and shows the first experimental evidence of a nonlinearly saturated phase instability mode for traveling wave patterns. At higher forcing level, this secondary pattern is subject to a tertiary instability. This mode is an amplitude mode characterized by traveling hole patterns, i.e., space-time defects that change the wave numbe

Supercritical transition to turbulence in an inertially-driven von Karman closed flow

We study the transition from laminar flow to fully developed turbulence for an inertially-driven von Karman flow between two counter-rotating large impellers fitted with curved blades over a wide range of Reynolds number (100 - 1 000 000). The transition is driven by the destabilisation of the azimuthal shear-layer, i.e., Kelvin-Helmholtz instability which exhibits travelling/drifting waves, modulated travelling waves and chaos below the emergence of a turbulent spectrum. A local quantity -the energy of the velocity fluctuations at a given point- and a global quantity -the applied torque- are used to monitor the dynamics. The local quantity defines a critical Reynolds number Rec for the onset of time-dependence in the flow, and an upper threshold/crossover Ret for the saturation of the energy cascade. The dimensionless drag coefficient, i.e., the turbulent dissipation, reaches a plateau above this finite Ret, as expected for a "Kolmogorov"-like turbulence for Re -> infinity. Our observations suggest that the transition to turbulence in this closed flow is globally supercritical: the energy of the velocity fluctuations can be considered as an order parameter characterizing the dynamics from the first laminar time-dependence up to the fully developed turbulence. Spectral analysis in temporal domain moreover reveals that almost all of the fluctuations energy is stored in time-scales one or two orders of magnitude slower than the time-scale based on impeller frequency

Ondes hydrothermales non-linéaires dans un disque et un anneau

URL: http://www-spht.cea.fr/articles/S98/109Nous nous intéressons à la convection thermocapillaire, produite par l'imposition d'un gradient {\it horizontal} de température sur une mince couche de fluide avec surface libre. En géométrie bidimensionnelle nous observons deux modes différents en compétition, tandis qu'en géométrie bidimensionnelle avec conditions limites périodiques, nous étudions la transition à la turbulence d'une onde propagative homogène

Fluctuation-Dissipation Relations and statistical temperatures in a turbulent von K\'arm\'an flow

We experimentally characterize the fluctuations of the non-homogeneous non-isotropic turbulence in an axisymmetric von K\'arm\'an flow. We show that these fluctuations satisfy relations analogous to classical Fluctuation-Dissipation Relations (FDRs) in statistical mechanics. We use these relations to measure statistical temperatures of turbulence. The values of these temperatures are found to be dependent on the considered observable as already evidenced in other far from equilibrium systems.Comment: four pages 2 figures one tabl

Experimental evidence of a phase transition in a turbulent swirling flow

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Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. II: Convective/absolute transitions

We present experimental results on hydrothermal waves in long and narrow 1D channels. In a bounded channel, we describe the primary and secondary instabilities leading to waves and modulated waves in terms of convective/absolute transitions. Because of on the combined effect of finite group velocity and of the presence of boundaries, the wave-patterns are non-uniform in space. We also investigate non-uniform wave-patterns observed in an annular channel in the presence of sources and sinks of hydrothermal waves. We connect our observations with the complex Ginzburg-Landau model equation in the very same way as in the first part of the paper (nlin.PS/0208029).Comment: 37 pages, 23 figures (elsart.cls + AMS extensions). Accepted in Physica D. See also companion paper "Nonlinear dynamics of waves and modulated waves in 1D thermocapillary flows. I: General presentation and periodic solutions" (nlin.PS/0208029). A version with high resolution figures is available on N.G. webpag

On the properties of steady states in turbulent axisymmetric flows

We experimentally study the properties of mean and most probable velocity fields in a turbulent von K\'arm\'an flow. These fields are found to be described by two families of functions, as predicted by a recent statistical mechanics study of 3D axisymmetric flows. We show that these functions depend on the viscosity and on the forcing. Furthermore, when the Reynolds number is increased, we exhibit a tendency for Beltramization of the flow, i.e. a velocity-vorticity alignment. This result provides a first experimental evidence of nonlinearity depletion in non-homogeneous non-isotropic turbulent flow.Comment: latex prl-stationary-051215arxiv.tex, 9 files, 6 figures, 4 pages (http://www-drecam.cea.fr/spec/articles/S06/008/